Quality of the mesh

There are numerous criteria for deciding the quality of a mesh [Geo91]. A few of these criteria as applicable to planar/surface meshes are -

1.

The variation in the area of the elements should not be too large.

2.

The aspect ratio of triangular elements should be as close to 1 as possible.
The aspect ratio of a triangular element is defined as the ratio of the circumradius of the triangle to twice its inradius. Hence the aspect ratio of an equilateral triangle is exactly 1.

3.

The ratio of the largest to the smallest edge/angle of the element should be close to 1.

4.

The ratio of the area of the largest/smallest element to all the immediate neighbours should not be drastically low/high.